In this example problem, we calculate the enthalpy of reaction using Hess's law. Our problem reads: Calculate the change in enthalpy for reaction 1 using the reactions provided below. To use Hess's law, we have to add together multiples of our reaction 2 and reaction 3 to produce reaction 1. First, we can look for the reaction that contains iron (III) oxide. We want 1 mole of iron (III) oxide as a reactant. Our reaction 3 has iron (III) oxide, but there are 2 moles and it's a product. So, to adjust reaction 3, we'll multiply by 1/2 and reverse the reaction. This way, we'll have 1 mole of iron (III) oxide as a reactant. When we reverse the reaction, we have to multiply the change in enthalpy for that reaction by -1. And when we multiply all of the coefficients by 1/2, we multiply the change in enthalpy for the reaction by 1/2. So, the overall result is -1/2 times the change in enthalpy for reaction 3. Next, we'll look for the reaction with carbon monoxide gas. Reaction 2 has 2 moles of carbon monoxide gas as a reactant, and we would like 3 moles of carbon monoxide gas as a reactant. So, we can multiply reaction 2 by 3/2 to obtain 3 moles of carbon monoxide gas as a reactant. We've used both reactions, so if we add these two reactions together, we should get reaction 1. When we add them together, we multiply the coefficients times our multipliers (1/2 and 3/2). All of the reactants go on the reactant side, and all of the products go on the product side in our overall reaction. In our overall reaction, we can cancel out anything that shows up on both sides. So, our 3/2 oxygen gas will cancel out from both sides, and we're left with iron (III) oxide plus 3 carbon monoxide produces 2 iron plus 3 carbon dioxide. To calculate the change in enthalpy for reaction 1, it will be -1/2 times the change in enthalpy for reaction 3 plus 3/2 times the change in enthalpy for reaction 2. If we substitute in our numbers and put this into our calculators, we should get -24 kilojoules.